Autocorrelation and memory allocation for wireless communication

ABSTRACT

Examples described herein include systems and methods which include wireless devices and systems with examples of an autocorrelation calculator. An electronic device including an autocorrelation calculator may be configured to calculate an autocorrelation matrix including an autocorrelation of symbols indicative of a first radio frequency (“RF”) signal and a second RF signal. The electronic device may calculate the autocorrelation matrix based on a stored autocorrelation matrix and the autocorrelation of symbols indicative of the first RF signal and symbols indicative of the second RF signal. The stored autocorrelation matrix may represent another received signal at a different time period than a time period of the first and second RF signals. Examples of the systems and methods may facilitate the processing of data for wireless and may utilize less memory space than a device than a scheme that stores and calculates autocorrelation from a large dataset computed from various time points.

CROSS REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of pending U.S. Patent applicationNo. 16/116,878 filed Aug. 29, 2018, which is a continuation of U.S.patent application Ser. No. 15/789,600 filed Oct. 20, 2017 and issued asU.S. Pat. No. 10,305,555 on May 28, 2019. The aforementionedapplications, and issued patent, are incorporated herein by reference,in its entirety, for any purpose.

BACKGROUND

There is interest in moving wireless communications to “fifthgeneration” (5G) systems. 5G promises increased speed and ubiquity, butmethodologies for processing 5G wireless communications have not yetbeen set. Implementing 5G systems may require more efficient use of thewireless spectra and memory consumption utilized in implementing such 5Gsystems.

Example 5G systems may be implemented using multiple-inputmultiple-output (MIMO) techniques, including “massive MIMO” techniques,in which multiple antennas (more than a certain number, such as 8 in thecase of example MIMO systems) are utilized for transmission and/orreceipt of wireless communication signals.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a wireless communications system arrangedin accordance with examples described herein.

FIG. 2 is a block diagram of an electronic device arranged in accordancewith examples described herein.

FIG. 3 is a flow diagram of a method arranged in accordance withexamples described herein.

FIG. 4 is a block diagram of a system arranged in accordance withexamples described herein.

FIG. 5 is a block diagram of a memory unit being accessed in accordancewith exampled described herein.

FIG. 6 is a block diagram of a computing device arranged in accordancewith examples described herein.

FIG. 7 is a block diagram of a wireless communications system arrangedin accordance with aspects of the present disclosure.

FIG. 8 is a block diagram of a wireless communications system arrangedin accordance with aspects of the present disclosure.

DETAILED DESCRIPTION

Traditional schemes to calculate an autocorrelation rely on large datasets to be computed from various time periods to calculate an accurateautocorrelation. Such processing may require cumbersome memory accessschemes to retrieve each relevant dataset for an overall calculation. Inaddition, memory storage is utilized to store such datasets inanticipation of such a calculation, requiring an increasingly largermemory footprint on devices that are an increasing in demand to beminiaturized. For example, an increasing demand for “Internet of Things”(IoT) devices may include miniaturization, while simultaneously includedemand for faster signal processing techniques.

The systems and methods described herein can be utilized to calculate anautocorrelation of a given signal using a dataset for a specific timeperiod. Advantageously, this may allow the autocorrelation to becalculated faster than conventional techniques and utilizing less memory(e.g., Flash or RAM) than conventional techniques that may wait toreceive several signals over multiple time periods. In an example, theautocorrelation of a specific time period is calculated and stored, andthen used again in a subsequent calculation of a next dataset withanother specific time period. By storing a value for each time period ofthe autocorrelation, less memory may be utilized than conventionalschemes that may utilize memory storage for information received duringeach time period.

Examples described herein include systems and methods which includewireless devices and systems with autocorrelation calculators which mayutilize an autocorrelation between multiple wireless channels togenerate an autocorrelation matrix. Such an autocorrelation matrix maybe updated at each time period to incorporate an autocorrelation matrixof a received signal at each respective time period. An autocorrelationmatrix of each received signal may be added to such a cumulativeautocorrelation matrix that may represent an overall autocorrelation ofthe received signals after multiple time periods.

in some examples, an autocorrelation calculator may be included in anelectronic device that includes multiple antennas. Receivers,transmitters, and/or transceivers described herein may receive theincident RF energy response to the indication that the wirelesscommunication is present in the portion of the wireless spectrum, andgenerate symbols that are autocorrelated in autocorrelation calculator.Radio frequency (RF) energy may be incident on multiple antennas (e.g. afirst and second antenna). The autocorrelation calculator may perform anautocorrelation calculation between symbols indicative of the RF energyreceived on the first and second antennas in a portion of the wirelessspectrum (e.g. at a particular frequency and/or frequency band) andcombine or incorporate (e.g., add) the result to a storedautocorrelation matrix. The RF energy received on the first and secondantenna in a portion of the wireless spectrum may be referred to as RFsignals from each antenna. The autocorrelation calculator may provide anupdated autocorrelation matrix that represents the storedautocorrelation matrix and the calculated autocorrelation matrixaccording to the symbols indicative of the RF energy received on thefirst and second antennas.

By using information from massive multi-input and multi-output (MIMO)systems described herein (which may be utilized in 5G wireless systems),examples described herein may utilize an autocorrelation betweendifferent MIMO transmission channels to calculate an autocorrelationmatrix for a specific time period. For example, such a calculatedautocorrelation may be utilized to calculate a set of weights to applyto incoming signals of a MIMO transceiver, in determining such weightswith a calculated autocorrelation, a MIMO system may utilize the set ofweights to more efficiently process, including at higher processedspeeds, incoming signals, with the weights compensating the incomingsignals in real-time. Such compensated signals may be further processedby the MIMO transceiver in accordance with any wireless application,such as beamforming applications, full-duplex applications, digital RFprocessing, and additional MIMO applications. In various examples,calculated autocorrelations may be utilized directly in suchapplications.

In an example of such an autocorrelation calculation to determine a setof weights for the calibration of a transceiver, the autocorrelation,R(N), of a known calibration signal, Y(N), may be utilized in a signalprocessing scheme to calculate the weights that relate the receivedsignal, X(N). X(N) may be a representation of the calibration signal,Y(N), at a transceiver, such as a MIMO transceiver including a MIMOantenna array. For example, X(N) may be an estimation of the calibrationsignal, Y(N) as received by a transceiver that may include wirelesschannel effects and noise from the transceiver. The received signal,X(N), may be represented as:

${X(N)} = \begin{pmatrix}{{x_{1}(1)},} & {{x_{2}(1)},} & \; & {x_{L}(1)} \\{{x_{1}(2)},} & {{x_{2}(2)},} & \; & {x_{L}(2)} \\\vdots & \vdots & \ldots & \vdots \\{{x_{1}(N)},} & {{x_{2}(N)},} & \; & {x_{L}(N)}\end{pmatrix}$

Each component, of the received signal may be received at an individualantenna, of which L antennas may receive the received signal, X(N). Forexample, each individual antenna may be a different antenna of a MIMOantenna array. N samples of each component of the received signal may bereceived over a time period of N length. For example, N length may be atime length, such as 10 ns, 10 ms, or 1 sec. The calibration signal,Y(N), can be referred to as a calibration signal matrix and may berepresented as:

${Y(N)} = \begin{pmatrix}{y(1)} \\{y(2)} \\\vdots \\{y(N)}\end{pmatrix}$

The autocorrelation, R(N), of the received signal may be computed viamatrix multiplication which may be represented as:

${R(N)} = {{{X^{T}(N)}{X(N)}} = \begin{pmatrix}{{r_{1}(1)},} & {{r_{2}(1)},} & \; & {r_{L}(1)} \\{{r_{1}(2)},} & {{r_{2}(2)},} & \; & {r_{L}(2)} \\\vdots & \vdots & \ldots & \vdots \\{{r_{1}(L)},} & {{r(L)},} & \; & {r_{L}(L)}\end{pmatrix}}$

In accordance with signal processing techniques described herein, a setof weights may be determined by matrix multiplication of the inverseautocorrelation matrix, R⁻¹(N) and a matrix, B(N), that represents thematrix multiplication of the transpose matrix of the received signalX^(T)(N) and the calibration signal, Y(N). For example, the set ofweights may be determined in accordance with the following equation:

${W = {{R^{- 1}(N)}{B(N)}}},{{{where}\mspace{14mu} W} = {{\begin{pmatrix}w_{1} \\w_{2} \\\vdots \\w_{L}\end{pmatrix}\mspace{14mu} {and}\mspace{14mu} {B(N)}} = {{{X^{T}(N)}{Y(N)}} = \begin{pmatrix}{b_{1}(N)} \\{b_{2}(N)} \\\vdots \\{b_{L}(N)}\end{pmatrix}}}}$

As described herein, examples of an autocorrelation calculation todetermine a set of weights for the calibration of a transceiver mayinclude a calculation of the autocorrelation, R(N). in an exampleautocorrelation calculation, the matrix R(N) may be computed inreal-time (e.g., as signals are received), with an updatedautocorrelation matrix being computed for each time period of a receivedsignal. This may include receiving, from each antenna of a plurality ofantennas, respective RF energies of a received signal at a time period.For example, the received signal may be represented as a vector at timeperiod N, with each L antenna receiving a component of the receivedsignal:

$\begin{pmatrix}{x_{1}(N)} \\{x_{2}(N)} \\\vdots \\{x_{L}(N)}\end{pmatrix}\quad$

Each component of the vector may represent a symbol(s) indicative of RFenergy received at each respective antenna. An autocorrelation matrixmay be calculated on the basis of autocorrelation such symbols andadding that autocorrelated matrix to a stored autocorrelation matrix.For example, the stored autocorrelation matrix may represent anautocorrelation of one or more received signals over various timeperiods. At a time period 0, the stored autocorrelation matrix may be azero matrix of size L×L, where L is a number of antennas. To perform acalculation utilizing the stored autocorrelation matrix, anautocorrelation calculation may be represented as:

${R(N)} = {{R\left( {N - 1} \right)} + {\begin{pmatrix}{x_{1}(N)} \\{x_{2}(N)} \\\vdots \\{x_{L}(N)}\end{pmatrix}\left( {{x_{1}(N)},{x_{2}(N)},{\ldots \mspace{14mu} {x_{L}(N)}}} \right)}}$

As an example, at a first time period (e.g., N=1), the autocorrelationmay be calculated as:

${R(1)} = {{R(0)} + {\begin{pmatrix}{x_{1}(1)} \\{x_{2}(1)} \\\vdots \\{x_{L}(1)}\end{pmatrix}\left( {{x_{1}(1)},{x_{2}(1)},{\ldots \mspace{14mu} {x_{L}(1)}}} \right)}}$

Accordingly, a stored autocorrelation matrix, R(0), may be retrievedfrom memory and added in matrix form to the autocorrelation of thesymbols indicative of RF energy received at each respective antenna atthat first time period. Advantageously, with the stored autocorrelationmatrix, R(0), occupying an L×L size of memory and with the vectorrepresentative of the symbols indicative of RF energy received at eachrespective antenna at that first time period occupying L size of memory,the amount of memory occupied in this autocorrelation calculation may beless than that of memory occupied when an autocorrelation is notcomputed at each time period.

For example, according to an autocorrelation calculation described abovewhere a signal or signals are received during N time periods for each Lantenna, the autocorrelation matrix may occupy an N×L amount of memory.Such an autocorrelation calculation may utilize more memory incalculating the autocorrelation than the autocorrelation calculation,described herein, in which each received signal vector in real-time isautocorrelated and added to a stored autocorrelation matrixrepresentative of the autocorrelation at a previous time period relativeto a current, real-time, time period of the received signal. In anexample of such a memory comparison, the autocorrelation calculationutilizing N×L amount of memory may represent a number of samplescorresponding to 4000 (e.g., N=4000) and a number of antennascorresponding to 16 (e.g., L=16), thereby occupying a 64k wordspace sizeof memory (e.g., 4000*16=64000). In contrast, the autocorrelationcalculation utilizing a stored autocorrelation matrix may represent areal-time calculation for a number of antennas corresponding to 16,thereby occupying a 272 wordspace size of memory (e.g., 16*16+16). Thatis, the stored autocorrelation matrix may occupy an L×L size of memory(e.g., 16*16) and the received signal vector in real-time may occupy anL size of memory (e.g., 16). Accordingly, the autocorrelationcalculation utilizing the stored autocorrelation matrix may utilize alesser amount of memory (e.g., fewer cells, a smaller portion of anarray, a smaller page size, a smaller word size, or the like) than theautocorrelation calculation occupying an N×L amount of memory.

As described herein, a stored autocorrelation matrix may represent theautocorrelation of previous received signals at previous time periods,Accordingly, R(1), may be representative of the symbols indicative of RFenergy received at each respective antenna at that first time period anda zero time period; and R(2), the symbols indicative of RF energyreceived at each respective antenna at the zero time period, the firsttime period, and the second time period. In accordance with theautocorrelation calculation described herein, R(2) may be calculated as:

${R(2)} = {{R(1)} + {\begin{pmatrix}{x_{1}(2)} \\{x_{2}(2)} \\\vdots \\{x_{L}(2)}\end{pmatrix}\left( {{x_{1}(2)},{x_{2}(2)},{\ldots \mspace{14mu} {x_{L}(2)}}} \right)}}$

In various examples, the autocorrelation matrix that was stored may beupdated after the addition of the stored autocorrelation matrix to theautocorrelation of the real-time vector. For example, the updatedautocorrelation matrix may be stored in the same memory space as thatfrom which the stored autocorrelation matrix was retrieved, therebyoccupying the same memory space while additional updated autocorrelationmatrices continue to be calculated. Each calculated autocorrelationmatrix may be referred to as a version of the autocorrelation, suchthat, for each time period, symbols indicative of the respective RFenergies may be autocorrelated, and combined with a respective versionof the autocorrelation matrix. For example, the respective version maybe the stored autocorrelation matrix at each previous time periodrelative to the time period in which the calculation occurs.Accordingly, the autocorrelation calculation described herein maycontinue to be computed in real-time, for example in the same memoryspace, with a calculation at time period N calculated as:

${R(N)} = {{R\left( {N - 1} \right)} + \ {\begin{pmatrix}{x_{1}(N)} \\{x_{2}(N)} \\\vdots \\{x_{L}(N)}\end{pmatrix}\left( {{x_{1}(N)},{x_{2}(N)},{\ldots \mspace{14mu} {x_{L}(N)}}} \right)}}$

Advantageously, in computing each version of the autocorrelation matrixand determining an overall autocorrelation matrix, a calculatedautocorrelation may be used in various applications for a wirelesstransceiver, such as for the determination of a set of weights forincoming signals. Accordingly, a transceiver may receive continuously anincoming signal over multiple time periods at a plurality of antennas.The calculated autocorrelation matrix may be utilized with a calibrationsignal to determine a set of weights, which may be utilized to generatean estimate of the information encoded in additional incoming signalsbased on the determined set of weights.

The benefits and various solutions introduced above are furtherdescribed below with reference to exemplary systems, apparatus, andmethods.

FIG. 1 is a block diagram of a wireless communications system arrangedin accordance with examples described herein. System 100 includeselectronic device 102 and electronic device 152. The electronic device102 includes an autocorrelation calculator 105, transceiver 120 coupledto antenna 106, transceiver 124 coupled to antenna 108, and transceiver128 coupled to antenna 110. The autocorrelation calculator 105 andtransceivers 120, 124, 128 may be in communication with one another.Each transceiver 120, 124, 128 may in communication with a respectiveantenna, such as antenna 106, antenna 108, and antenna 110. Theelectronic device 152 includes an autocorrelation calculator 155, thetransceiver 126 coupled to antenna 162, the transceiver 130 coupled tothe antenna 164, and the transceiver 132 coupled to the antenna 166. Theautocorrelation calculator 155 and transceivers 126, 130, 132 may be incommunication with one another. Each transceiver 126, 130, 132 may incommunication with a respective antenna, such as antenna 162, antenna164, and antenna 166. In other examples, fewer, additional, and/ordifferent components may be provided. For example, while described abovewith each antenna coupled to respective transceiver, in other examples,multiple antennas may be coupled to a single transceiver of anelectronic device. In the example of electronic device 102, while notdepicted, the antennas 106, 108, 110 may be coupled to a singletransceiver 120 of the electronic device 102, with no transceivers 124,128 included in that example.

Electronic devices described herein, such as electronic device 102 andelectronic device 152 shown in FIG. 1 may be implemented using generallyany electronic device for which wireless communication capability isdesired. For example, electronic device 102 and/or electronic device 152may be implemented using a mobile phone, smartwatch, computer (e.g.server, laptop, tablet, desktop), or radio. In some examples, theelectronic device 102 and/or electronic device 152 may be incorporatedinto and/or in communication with other apparatuses for whichcommunication capability is desired, including devices associated withthe Internet of Things (IoT), such as but not limited to, an automobile,airplane, helicopter, appliance, tag, camera, or other device.

While not explicitly shown in FIG. 1, electronic device 102 and/orelectronic device 152 may include any of a variety of components in someexamples, including, but not limited to, memory, input/output devices,circuitry, processing units (e.g. processing elements and/orprocessors), or combinations thereof. Additionally or alternatively, theelectronic devices 102 and 152 may include microphones coupled to arespective transceiver replacing or in addition to the antennas 106-110and antennas 162-166. example, a microphone array may be coupled to asingle transceiver in the electronic device 102 or each microphone ofthe microphone array may be coupled to a respective transceiver 120,124, 128 of the electronic device 102, like the antennas 106-110.

The electronic device 102 and the electronic device 152 may each includemultiple antennas. For example, the electronic device 102 and electronicdevice 152 may each have more than two antennas. Three antennas each areshown in FIG. 1, but generally any number of antennas may be usedincluding 2, 3. 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 32, 64, or96 antennas. Other numbers of antennas may be used in other examples. Insome examples, the electronic device 102 and electronic device 152 mayhave a same number of antennas, as shown in FIG. 1, In other examples,the electronic device 102 and electronic device 152 may have differentnumbers of antennas. Generally, systems described herein may includeMIMO systems.

MIMO systems generally refer to systems including one or more electronicdevices which transmit transmissions using multiple antennas and one ormore electronic devices which receive transmissions using multipleantennas. In some examples, electronic devices may both transmit andreceive transmissions using multiple antennas. Some example systemsdescribed herein may be “massive MIMO” systems. Generally, massive MIMOsystems refer to systems employing greater than a certain number (e.g.96) antennas to transmit and/or receive transmissions. As the number ofantennas increase, so to generally does the complexity involved inaccurately transmitting and/or receiving transmissions. Although twoelectronic devices (e.g. electronic device 102 and electronic device152) are shown in FIG. 1, generally the system 100 may include anynumber of electronic devices.

Electronic devices described herein may include receivers, transmitters,and/or transceivers. For example, the electronic device 102 of FIG. 1includes transceiver 120 and the electronic device 152 includestransceiver 126. Generally, receivers may be provided for receivingtransmissions from one or more connected antennas, transmitters may beprovided for transmitting transmissions from one or more connectedantennas, and transceivers may be provided for receiving andtransmitting transmissions from one or more connected antennas.

The transmissions described herein may be in accordance with any of avariety of protocols, including, but not limited to 5G signals, and/or avariety of modulation/demodulation schemes may be used , including, butnot limited to: orthogonal frequency division multiplexing (OFDM),filter bank multi-carrier (FBMC), the generalized frequency divisionmultiplexing (GFDM), universal filtered multi-carrier (UFMC)transmission, bi orthogonal frequency division multiplexing (BFDM),sparse code multiple access (SCMA), non-orthogonal multiple access(NOMA), multi-user shared access (MUSA) and faster-than-Nyquist (FTN)signaling with time-frequency packing. In some examples, thetransmissions may be sent, received, or both, in accordance with 5Gprotocols and/or standards. Generally, multiple receivers, transmitters,and/or transceivers may be provided in an electronic device one incommunication with each of the antennas of the electronic device. Forexample, the transceiver 124 may be used to provide transmissions toand/or receive transmissions from antenna 108, while other transceiversmay be provided to provide transmissions to and/or receive transmissionsfrom antenna 106 and antenna 110.

Examples of transmitters, receivers, and/or transceivers describedherein, such as the transceiver 120 and transceiver 124 may beimplemented using a variety of components, including, hardware,software, firmware, or combinations thereof. For example, transceiversmay include circuitry and/or one or more processing units (e.g.processors) and memory encoded with executable instructions for causingthe transceiver to perform one or more functions described herein (e.g.software).

Autocorrelation calculators described herein, may calculate anautocorrelation matrix of a received signal of an electronic device. So,for example, the electronic device 152 may include three transceivers,including the transceivers 126, 130, 132, to service antennas 162, 164,166, respectively. The autocorrelation calculator 155 may be incommunication with multiple (e.g. all) of the transceivers of theelectronic device 152, and may calculate an autocorrelation utilizingsymbols indicative of the RF signals received at the antenna 112,antenna 114, and antenna 116.

It may be desirable in some examples to utilize a calculatedautocorrelation in real-time to avoid some issues faced with traditionalautocorrelation schemes. For example, and as discussed above, atraditional autocorrelation scheme may queue or store received signalsover multiple time periods in a memory space to calculate an overallautocorrelation of those received signals at a later point in time;often utilizing a large memory space to make such a computation. As usedherein, each time period of a real-time calculation may be related to atime in which a particular signal is received or a queue length of theautocorrelation calculator described herein. In the latter case, forexample, the queue may hold a portion of a received signal and thus thatportion of the received signal may be computed in that time period,defined by the length of the queue. This can be referred to as areal-time calculation of the portion of the received signal in anautocorrelation calculation. In such a way, queues may utilize smallermemory spaces.

In some examples, the time period may be related to the sampling periodof the samples received during that sampling period or a symbol periodof the symbols received during that symbol period, for example,depending on whether a sample or symbol is to be computed as part of theautocorrelation matrix. in a traditional autocorrelation scheme, anautocorrelation may not be calculated until all N samples of thesampling period (or all N symbols of symbol period) for each antenna arereceived. In such a scheme, the previous N−1 samples (or N−1 symbols)for each antenna are stored in the memory; and the calculation of anautocorrelation may only start when the N′th sample (or N′th symbol) isreceived. In a real-time calculation, as referred to herein, anautocorrelation matrix may be calculated, when each sample (or symbol)is received at each antenna, for example, by adding a storedautocorrelation matrix to the calculated autocorrelation matrix of thatsample received at each antenna, at that time. This iterativecalculation may continue to occur during an overall respective sample orsymbol time period when further samples or symbols are expected to bereceived at each antenna, until the respective N′th sample or N′thsymbol is received.

It may be desirable for one or more electronic devices described hereinto utilize a smaller memory space than a queuing scheme of theaforementioned example utilizing a traditional autocorrelation schemeand queuing over multiple time periods. In some examples, a smallermemory space may occupy an amount of memory related to the number ofantennas, rather than an amount of memory related to the number ofantennas and the number of samples acquired of the received signal.Particularly as wireless communications incorporate 5G standards,miniaturization of devices may become increasingly desirable, thuslimiting the memory space available for some applications, such as acomputation of an autocorrelation of received signals.

Accordingly, electronic devices described herein may include one or moreautocorrelation calculators. For example, the electronic device 102 mayinclude the autocorrelation calculator 105, and the electronic device152 may include the autocorrelation calculator 155. Examples ofautocorrelation calculators described herein may utilize symbolsreceived from transceivers of the electronic devices 150, 152 tocalculate autocorrelation matrices at time periods in which thetransceivers receive signals communicated via respective, coupledantennas.

Examples of autocorrelation calculators described herein, including theautocorrelation calculator 105 and the autocorrelation calculator 155 ofFIG. 1 may be implemented using hardware, software, firmware, orcombinations thereof. For example, the autocorrelation calculator 105and the autocorrelation calculator 155 may be implemented usingcircuitry and/or one or more processing unit(s) (e.g. processors) andmemory encoded with executable instructions for causing theautocorrelation calculator to perform one or more functions describedherein.

FIG. 2 is a schematic illustration of an electronic device 202 arrangedin. accordance with examples described herein. The transceiver 220 maybe coupled to antenna 206 and may have a receive path 204. Thetransceiver 228 may be coupled to antenna 210 and may have a receivepath 214. Each receive path 204 and receive path 214 may include ananalog-to-digital converter (“ADC”) coupled to a respective antenna(e.g., antenna 206 or antenna 210), followed by a digital down-converter(“DDC”), a cyclic prefix remover, a transform (e.g. a discrete Fouriertransform, or “DFT”) and an adding removal component. Transmit paths ofthe transceivers 220, 228 may each include an adding component, aninverse transform (e.g. an inverse Fourier transform), a digitalup-converter (“DUC”), and a digital-to-analog converter coupled to arespective antenna (e.g., antenna 206 or antenna 210). In the example,the adding component may add an additional processing field to data inthe transmit path, such as a guard interval period, a post-processingfield, a sampling field, or a filtering field. In some examples, adecoder and/or precoder may be coupled to the respective receive paths204, 214, respectively, before symbols are provided to theautocorrelation calculator 205. The transceiver 220 or transceiver 228may be used to implement and/or be implemented by example transceiversdescribed herein, such as the transceivers 120, 124, 128 and/or thetransceivers 126, 130, 132 of FIG. 1. Transceiver 228 may be coupled toantenna 210 and may have a receive path 214 and a transmit path. In someexamples, additional, fewer, and/or different components may beincluded. Generally one transceiver may be provided for each antennaused in an electronic device. Any L number of transceivers may beincluded in the electronic device 202, with the transceiver 228 beingindicated as the Lth transceiver. In such cases, additional receivepaths may be provided to the autocorrelation calculator 205.

The autocorrelation calculator 205 may receive symbols indicative of RFenergy from the transceivers 220, 228 via the respective receive paths204, 214. Components of the receive path 204 and/or receive path 214 maybe implemented using circuitry (e.g. analog circuitry) and/or digitalbaseband circuitry in some examples, The autocorrelation calculator 205may provide a calculated autocorrelation matrix. For example, theautocorrelation calculator may receive various components of a receivedsignal from the receive paths 204, 214, such as a received signal fromeach antenna 206-210 including respective RF energies of the receivedsignal at that time period. For example, the received signal may berepresented as a vector at time period N, with each L antenna receivinga component of the received signal:

$\begin{pmatrix}{x_{1}(N)} \\{x_{2}(N)} \\\vdots \\{x_{L}(N)}\end{pmatrix}\quad$

In the example of FIG. 2, the receive path 204 may include thecomponent, x_(l)(N), that represents a symbol(s) indicative of RF energyreceived at antenna 206, while the receive path 214 may include thecomponent, x_(l)(N), that represents a symbol(s) indicative of RF energyreceived at antenna 210. An autocorrelation matrix may be calculated onthe basis of autocorrelation such symbols and adding that autocorrelatedmatrix to a stored autocorrelation matrix. To perform a calculationutilizing the stored autocorrelation matrix and the received signal atantennas 206-210, an autocorrelation calculation may be represented as:

${R(N)} = {{R\left( {N - 1} \right)} + \ {\begin{pmatrix}{x_{1}(N)} \\{x_{2}(N)} \\\vdots \\{x_{L}(N)}\end{pmatrix}\left( {{x_{1}(N)},{x_{2}(N)},{\ldots \mspace{14mu} {x_{L}(N)}}} \right)}}$

Accordingly, a stored autocorrelation matrix, R(N−1), may be retrievedfrom memory and combined in matrix form with the autocorrelation of thesymbols indicative of RF energy received at each respective antenna206-210 at the first time period in which the received signal isreceived. Advantageously, with the stored autocorrelation matrix,R(N−1), occupying an L×L size of memory and with the vectorrepresentative of the symbols indicative of RF energy received at eachrespective antenna at the first time period occupying L size of memory,the amount of memory occupied in this autocorrelation calculation may beless than that of traditional autocorrelation schemes, for example, asdescribed above, with respect to the example of an autocorrelationscheme utilizing an N×L size of memory.

Examples of autocorrelation calculators described herein, such as theautocorrelation calculator 205 may receive information from a number ofwireless communication channels (e.g., receive paths 204, 214). Anynumber of antennas (and corresponding inputs to the autocorrelationcalculator 205) may be used. Accordingly, time-domain symbols may beprovided to the autocorrelation calculator 205. Referring back to FIG.1, for example, the autocorrelation calculator 105 may receive symbolsindicative of RF energy in a portion of the wireless spectrum incidenton antenna 106, antenna 108, and/or antenna 110. A corresponding one ofthe transceivers 120, 124, 128 may process the symbols indicative of RFenergy in a portion of the wireless spectrum to generate time-domainsymbols indicative of data of control information. The autocorrelationcalculator 105 may receive the symbols processed by the transceivers forcalculation of an autocorrelation matrix, for example, received viarespective receive paths of the transceivers 120, 124, 128.

Any portion of the wireless spectrum may be utilized in computingautocorrelation matrices. For example, the antennas may be tuned to aparticular frequency and/or frequency band, and consequently the dataprovided by those antennas may relate to that particular frequencyand/or frequency band. Examples of frequency bands include thoselicensed by the FCC, and generally may include any RF frequencies.Generally, RF frequencies may range from 3 Hz to 3000 GHz in someexamples. In some examples, a particular band may be of interest.Examples of bands include all or portions of a very high frequency (VHF)band (e.g. 30-300 Mhz), all or portions of an ultra high frequency (UHF)band (e.g. 300-3000 MHz), and/or all or portions of a super highfrequency (SHF) band (e.g. 3-30 GHz). Example bands may include 5Gwireless frequency ranges, such as utilizing a carrier frequency in theE band (e.g., 71 76 GHz and 81-86 GHz), a 28 GHz Millimeter Wave(mmWave) band, or a 60 GHz V band (e.g., implementing a 802.11 adprotocol). Example autocorrelation calculators may calculate matricesbased on RF energy from a portion of a wireless spectrum of generallyany width (e.g. 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 or more MHzwidths). The analog to digital conversion operation in receive paths204, 214 may convert RF energy from an analog signal to a digital RFsignal.

The digital down conversion operation in receive paths 204, 214 may downconvert frequency domain symbols at a certain frequency band to abaseband processing range. In examples where signals may be received bythe transceiver 220, 228, the time-domain symbols may be mixed with alocal oscillator frequency to generate 5G symbols at a basebandfrequency range. Accordingly, the RF energy that may include time-domainsymbols may be digitally down-converted to baseband. The adding removalcomponent in the receive paths 204, 214 may remove an added processingfield from the baseband data, such as a guard interval, from thefrequency-domain 5G symbols. A DFT operation in the receive paths 204,214 may be implemented as an FFT operation that transforms thetime-domain symbols into frequency-domain symbols. For example, takingan example of an OFDM wireless protocol scheme, the FFT can be appliedas N-point FFT

$\begin{matrix}{X_{n} = {\sum\limits_{k = 1}^{N}{x_{k}e^{{- t}\; 2\; \pi \; {{kn}/N}}}}} & (12)\end{matrix}$

where X_(n) is the modulated symbol sent in the nth OFDM sub-carrier.Accordingly, the output of the FFT operation may form frequency-domainOFDM symbols. In some examples, the FFT may be replaced by poly-phasefiltering banks to output symbols for the synchronization operation.

As described herein, the operations of the electronic device 202 caninclude a variety of RF processing operations performed with analogcircuits and/or digital implementations of analog circuits. Suchoperations can be implemented in a conventional wireless transceiver,with each operation implemented by specifically-designed hardware forthat respective operation. For example, a DSP processing unit may bespecifically-designed to implement the FFT operation. As can beappreciated, additional operations of a wireless transceiver may beincluded in a conventional wireless transceiver, and some operationsdescribed herein may not be implemented in a conventional wirelessreceiver. Accordingly, while specific components are not depicted inFIG. 2 that represent a corresponding specifically-designed hardwarecomponent of a transceiver 220, 228, it can be appreciated that theelectronic device 202 may include such components and process thesymbols indicative of RF energy as described herein.

In calculating an autocorrelation matrix in accordance with the examplesdescribed herein, the autocorrelation calculator 205 may determine a setof weights based on the calculated, cumulative autocorrelation matrix.The set of weights may be utilized to compensate received signalsreceived at antennas 206-210 for the effects of the wireless channel,noises introduced by the electronic device 202, or any other effect thatmay alter a calibration signal utilizing in calibrating the electronicdevice 202. The electronic device 202. may utilize a calibration signal,as described herein, for the determination of the set of weights to beutilized in compensating RF energies received at the electronic device202. Advantageously, in calibrating the electronic device 202 or inreceiving received signals to which a set of weights are applied, theautocorrelation calculator 205 may calculate autocorrelation matriceswith increased speed, while also utilizing less memory space.

Accordingly, for electronic devices that change operating environmentsquickly, the autocorrelation calculator 205 may continue to calculateand update a set of weights to be applied to receive signals. Forexample, a mobile device rendering video may change environmentsquickly. By calibrating a new set of weights in that new environment atspecific time periods with a piece-wise autocorrelation matrix, themobile device may render the video more quickly than a traditionalautocorrelation scheme. The mobile device may utilized updated versionsof the autocorrelation matrix to determine a set of weights, forexample.

FIG. 3 is a flowchart of a method 300 in accordance with examplesdescribed herein. Example method 300 may be implemented using, forexample, system 100 in FIG. 1, electronic device 202 in FIG. 2, system400 in FIG. 4, or any system or combination of the systems depicted inFIGS. 1-2 and 4-8 described herein. The operations described in blocks308-324 may also be stored as computer-executable instructions in acomputer-readable medium such as memory units (e.g., memory unit 440 a).

Example method 300 may begin the autocorrelation method. At block 308,the method 300 may include receiving from each antenna of a plurality ofantennas respective RF energies of a plurality of signals. For example,in the context of FIG. 2, antennas 206, 210 may receive respective RFenergies (e.g., RF signals at respective portions of the wirelessspectrum. In the example, the RF signals may be processed by therespective transceivers 220, 228. At block 312, the method 300 mayinclude retrieving a stored autocorrelation matrix representative ofanother plurality of signals. For example, in the context of FIG. 4, anautocorrelation calculator 405 may retrieve a stored autocorrelationmatrix from the memory unit 440 a or the memory unit 440 b. The storedautocorrelation matrix may occupy a space in one of the memory units 440a, 440 b that is related to a number of antennas. For example, thenumber of antennas may be a number of antennas coupled to an electronicdevice 202. In the example, the autocorrelation calculator 405 mayrequest the stored autocorrelation matrix from a memory that is part ofan implementing computing device (e.g., electronic device 202), from amemory part of an external computing device, or from a memoryimplemented in a cloud-computing device. In turn, the memory may sendthe stored autocorrelation matrix as requested by the autocorrelationcalculator 405.

At block 316, the method 300 may include calculating an autocorrelationmatrix based on the stored autocorrelation matrix and symbols indicativeof RF energies. For example, in the context of FIG. 4, anautocorrelation calculator 405 may occupy a memory space to perform acalculation with an autocorrelation matrix and a signal received at aplurality of antennas. The symbols indicative of the RF energies may berepresentative of the signal received at the plurality of antennas. Asdescribed herein, to calculate the autocorrelation matrix, the symbolsindicative of the respective RF energies may be autocorrelated, andcombined with (e.g., added) a respective version of the autocorrelationmatrix, for example, the stored autocorrelation matrix. The memory spacein which the calculation is performed may include the memory space fromwhich the stored autocorrelation matrix was received. The calculatedautocorrelation matrix may be based on the stored autocorrelation matrixand the signal received at the plurality of antennas. The calculatedautocorrelation matrix may be referred to as an updated autocorrelationmatrix. For example, the stored autocorrelation matrix may not beutilized in subsequent calculations. The updated autocorrelation matrixmay be utilized as a stored autocorrelation matrix in subsequentcalculations, once it has been stored.

At block 320, the method 300 may include storing the autocorrelationmatrix. For example, in the context of FIG. 4, an autocorrelationcalculator 405 may store the autocorrelation matrix in the memory unit440 a or the memory unit 440 b. The autocorrelation matrix that isstored may be an updated autocorrelation matrix. In some examples, theupdated autocorrelation matrix may be stored in the memory space inwhich the stored autocorrelation matrix was retrieved. To store theautocorrelation matrix, the autocorrelation calculator may provide amemory command associated with storing the updated autocorrelationmatrix in the memory space to the memory unit 440 a or the memory unit440 b via, respective, memory interfaces 435 a, 435 b. Thereafter, block320 may be followed by block 324 that ends the method 300.

The blocks included in the described example method 300 are forillustration purposes. In some examples, the blocks may be performed ina different order. In some other examples, various blocks may beeliminated. In still other cases, various blocks may be divided intoadditional blocks, supplemented with other blocks, or combined togetherinto fewer blocks. Other variations of these specific blocks arecontemplated, including changes in the order of the blocks, changes inthe content of the blocks being split or combined into other blocks,etc.

FIG. 4 is a block diagram of a computing system 400 arranged inaccordance with examples described herein. The computing system 400includes an autocorrelation calculator 405 coupled to memory units 440a, 440 b. The autocorrelation calculator 405 may implement a memorycontroller 410 to retrieve, calculate, and store autocorrelationmatrices. The memory controller 410 may be coupled to the memory units440 a, 440 b via memory interfaces 435 a, 435 b. The memory controller410 may implement memory commands received from various data sources orprocesses being executed on the autocorrelation calculator 405. Forexample, the memory controller 410 may receive memory access requests(e.g., read or write commands) from a process being executed on theautocorrelation calculator 405. In such a case, the memory controller410 may process the memory access requests, as implemented by theautocorrelation calculator 405, to access one or more of the memoryunits 440 a, 440 b.

The autocorrelation calculator 405 may be used to implement a computingsystem utilizing the memory controller 410. The autocorrelationcalculator 405 may be a multi-core processor in some examples thatincludes a plurality of cores. The plurality of cores may for example beimplemented using processing circuits which read and execute programinstructions independently. The memory controller 410 may handlecommunication with the memory system that may be outside of theautocorrelation calculator 405. For example, the memory controller 410may provide access commands to the memory units 440 a, 440 b from theplurality of cores of the autocorrelation calculator 405. The memorycontroller 410 may provide such access commands via memory interfaces435 a, 435 b. For example, the memory interfaces 435 a, 435 b mayprovide a clock signal, a command signal, and/or an address signal toany of the memory units 440 a, 440 b. While writing data by storing thedata in the memory units 440 a, 440 b, the memory controller 410provides instructions to write data to the memory units 440 a, 440 bbased on a write command. While reading the stored data from the memoryunits 440 a, 440 b, the memory controller 410 provides instructionsbased on a read command and receives the data from the memory units 440a, 440 b.

The memory controller 410 may be implemented using circuitry whichcontrols the flow of data to the memory units 440 a, 440 b. The memorycontroller 410 may be a separate chip or integrated circuit coupled tothe autocorrelation calculator 405 or being implemented. on theautocorrelation calculator 405, for example, as a core of theautocorrelation calculator 405 to control the memory system of thecomputing system 400. In some examples, the memory controller 410 may beintegrated into the autocorrelation calculator 405 to be referred to asintegrated memory controller (IMC).

The memory controller 410 may communicate with a plurality of memoryunits to implement a memory system with the autocorrelation calculator405. For example, the memory units 440 a, 440 b, may communicatesimultaneously with the memory controller 410. While the example of FIG.4 depicts two memory units 440 a, 440 b, it can be expected that thememory controller 410 may interact with any number of memory units. Forexample, eight memory units may be included and each memory unit mayinclude a data bus having an eight-bit width, thus the memory systemimplemented by the autocorrelation calculator 405 may have a sixty-fourbit width. The memory units 440 a, 440 b may be dynamic random-accessmemory (DRAM) or nonvolatile random-access memory (RAM), such as staticRAM (SRAM), ferroelectric RAM (FeRAM), spin-transfer-torque RAM(STT-RAM), phase-change RAM (PCRAM), resistance change RAM (ReRAM),phase change memory, 3D XPoint, or the like. In an exampleimplementation, the memory unit 440 a may correspond to a cache and/orSRAM and the memory unit 440 b may correspond to DRAM. Because of thelesser memory space utilized in the autocorrelation schemes describedherein, the memory controller 410 may determine to control only thememory unit 440 a with the cache and/or SRAM to perform theautocorrelation calculations. In other example implementations, thememory controller 410 may increase the speed of autocorrelationcalculation in utilizing both memory units 440 a, 440 b. For example,the memory unit 440 a may be utilized as storage for a version of theautocorrelation matrix, and the memory unit 440 b may be utilized toperform the autocorrelation calculation including storage of the symbolsindicative of the RF energies received at the plurality of antennasqueued in the DRAM.

In various examples, such memory units may be referred to as memorychips, memory modules, memory dies, memory cards, memory devices, memoryarrays, and/or memory cells. Physically, the memory units 440 a, 440 bmay be arranged and disposed as one layer, or may be disposed as stackedlayers. In some examples, the memory units 440 a, 440 b may be disposedas multiple layers, on top of each other, to form vertical memory, suchas 3D NAND Flash memory.

In some examples where the memory units 440 a, 440 b may be implementedusing DRAM or non-volatile RAM integrated into a single semiconductorchip, the memory units 440 a, 440 b may be mounted on a memory modulesubstrate, a mother board or the like. For example, the memory units 440a, 440 b be referred to as memory chips. The memory units 440 a, 440 bmay include a memory cell array region and a peripheral circuit region.The memory cell array region includes a memory cell array with aplurality of banks, each bank including a plurality of word lines, aplurality of bit lines, and a plurality of memory cells arranged atintersections of the plurality of word lines and the plurality of bitlines. The selection of the bit line may be performed by a plurality ofcolumn decoders and the selection of the word line may be performed by aplurality of row decoders.

The peripheral circuit region of the memory units 440 a, 440 b mayinclude clock terminals, memory address terminals, command terminals,and data input/output (I/O) terminals (DQ). For example, the data I/Oterminals may handle eight-bit data communication. Data input output(I/O) buffers may be coupled to the data input/output terminals (DQ) fordata accesses, such as read accesses and write accesses of memories. Thememory address terminals may receive address signals and bank addresssignals. The bank address signals may be used for selecting a bank amongthe plurality of banks. A row address and a column address may beprovided as address signals. The command terminals may include a chipselect (/CS) pin, a row address strobe (/RAS) pin, a column addressstrobe (/CAS) pin, a write enable (/WE) pin, and/or the like. A commanddecoder may decode command signals received at the command terminalsfrom the memory controller 410 via one of the memory interfaces 435 a,435 b to receive various commands including a read command and/or awrite command. Such a command decoder may provide control signalsresponsive to the received commands to control the memory cell arrayregion. The clock terminals may be supplied with an external clocksignal, for example from one of the memory interfaces 435 a, 435 b.

While the computing system 400 has been described in the context of animplementation of the autocorrelation calculator 405, it can be expectedthat the computing system 400 may also be implemented differently inother examples. For example, the computing system 400 may be included ineither of the electronic devices 102, 152 or 202. of FIGS. 1 and 2,respectively. The autocorrelation calculators 105, 155, 204 may beimplemented as the autocorrelation calculator 405, for example. In thecontext of FIG. 2, the autocorrelation calculator 205, implemented asthe autocorrelation calculator 405, may be coupled to transceivers 220,228 as a separate circuit such as an application specific integratedcircuits (ASIC), a digital signal processor (DSP) implemented as part ofa field-programmable gate array (FPGA), or a system-on-chip (SoC).Additionally or alternatively, the autocorrelation calculator 405 may beimplemented using any system or combination of the systems depicted inFIGS. 1-2 and 4-8 described herein.

FIG. 5 is a block diagram of a memory unit 540 being accessed inaccordance with exampled described herein. The memory cells of thememory unit 540, which include memory cells labeled as A1-A4, C1-C4, andD1-D4 and memory cells 560 labeled as N1-N4, are schematicallyillustrated in a memory system 500. In the example of FIG. 5, the memoryunit 540 may be a memory array including the memory cells 550. Thememory system 500 receives a memory command for retrieval, calculation,or storage of an autocorrelation matrix. For example, a memorycontroller implemented in or in conjunction with an autocorrelationcalculator, such as the memory controller 410 in the autocorrelationcalculator 405 of FIG. 4, may access the memory cells 550 and 560 forcalculation of an autocorrelation matrix.

In the context of FIG. 4, an autocorrelation calculator 405 may retrieve(e.g., read request) a stored autocorrelation matrix from the memoryunit 540 stored in the memory cells 550, for example. During acalculation of an autocorrelation matrix, memory controller 410 may alsorequest access to memory cells 560 to queue or occupy a memory space fora received signal. For example, in the context of FIG. 2, each memorycell N1-N4 560 may provide a memory space for a corresponding componentof a received signal. For example, in the context of FIG. 2, if thenumber of antennas of the electronic device included four antennas, thereceive path 204 may include the component, x_(l)(N), that represents asymbol(s) indicative of RF energy received at antenna 206, while thereceive path 214 may include the component, x_(L)(N), that represents asymbol(s) indicative of RF energy received at antenna 210. The componentx_(l)(N) may occupy the memory cell N1 and the component x_(L)(N) mayoccupy the memory cell N4. In the example, additional componentsreceived from the other two antennas (not depicted in FIG. 2) may occupymemory cells N2 and N3. Because the number of antennas in the example isfour antennas, a stored autocorrelation matrix be a size of 4×4 matrix,occupying the memory space corresponding to the memory cells 550.

The amount or quantity of memory cells accessed may be related to anumber of antennas. For example, the stored autocorrelation matrix mayoccupy the memory cells 500 which is related to a number of antennas.For example, the number of antennas may be a number of antennas coupledto an electronic device 202. In the example, the autocorrelationcalculator 405 may request the stored autocorrelation matrix from thememory cells 550. In turn, the memory unit 540 may provide the storedautocorrelation matrix as requested by the autocorrelation calculator405. The memory space (e.g., memory cells 550, 560) in which thecalculation is performed may include the memory space from which thestored autocorrelation matrix was received (e.g., memory cells 550).

A calculated autocorrelation matrix may be stored (e.g., a writerequest) in the same memory space from which the stored autocorrelationmatrix was retrieved—the memory cells 500. Once stored in the memorycells 500, this calculated autocorrelation matrix may be referred to asan updated autocorrelation matrix and may be utilized as a storedautocorrelation matrix in subsequent calculations. Additionally oralternatively, in subsequent calculations, the memory cells 560 may beutilized again to read/write or occupy a received signal from adifferent time period. Accordingly, the memory cells 550, 560 of thememory unit 540 may be accessed for retrieval, calculation, or storagein accordance with the examples described herein related to thecalculation of an autocorrelation matrix.

While described in FIG. 5 in the context of a two-dimensional memoryarray, it can be expected that memory access commands may be configuredfor memory in a three-dimensional or N-dimensional space; for example,to process matrix operations with corresponding memory commands in thatthree-dimensional or N-dimensional space.

FIG. 6 is a block diagram of a computing device 600 arranged inaccordance with examples described herein. The computing device 600 mayoperate in accordance with any example described herein. The computingdevice 600 may implemented in a smartphone, a wearable electronicdevice, a server, a computer, an appliance, a vehicle, or any type ofelectronic device. The computing device 600 includes a memory system602, an autocorrelation calculator 605, and I/O interface 670, and anetwork interface 690 coupled to a network 695. The memory system 602includes a memory controller 610. Similarly numbered elements of FIG. 6include analogous functionality to those numbered elements of FIGS. 4-5.For example, the memory units 640 may operate and be configured like thememory units 440 a, 440 b of FIG. 4 or memory unit 540 of FIG. 5.Autocorrelation calculator 605 may include any type of microprocessor,central processing unit (CPU), an application specific integratedcircuits (ASIC), a digital signal processor (DSP) implemented as part ofa field-programmable gate array (FPGA), a system-on-chip (SoC), or otherhardware to provide processing for device 600.

The memory system 602 includes memory units 540, which may benon-transitory hardware readable medium including instructions,respectively, for calculating an autocorrelation matrix or be memoryunits for the retrieval, calculation, or storage of an autocorrelationmatrix. The autocorrelation calculator 605 may control the memory system602 with control instructions that indicate when to execute such storedinstructions for calculating an autocorrelation matrix or for theretrieval or storage of an autocorrelation matrix. Upon receiving suchcontrol instructions, the memory controller 610 may execute suchinstructions. For example, such instructions may include a program thatexecutes the method 300. Communications between the autocorrelationcalculator 605, the I/O interface 670, and the network interface 690 areprovided via an internal bus 680. The autocorrelation calculator 605 mayreceive control instructions from the I/O interface 670 or the networkinterface 690, such as instructions to calculate an autocorrelationmatrix.

Bus 680 may include one or more physical buses, communicationlines/interfaces, and/or point-to-point connections, such as PeripheralComponent Interconnect (PCI) bus, a Gen-Z switch, a CCIX interface, orthe like. The FO interface 670 can include various user interfacesincluding video and/or audio interfaces for the user, such as a tabletdisplay with a microphone. Network interface 690 communications withother computing devices, such as computing device 600 or acloud-computing server, over the network 695. For example, the networkinterface 690 may be a USB interface.

FIG. 7 is a block diagram of a wireless communications system 700 inaccordance with aspects of the present disclosure. The wirelesscommunications system 700 includes a base station 710, a mobile device715, a drone 717, a small cell 730, and vehicles 740, 745. The basestation 710 and small cell 730 may be connected to a network thatprovides access to the Internet and traditional communication links. Thesystem 700 may facilitate a wide-range of wireless communicationsconnections in a wireless communication (e.g., 5G) system that mayinclude various frequency bands, including but not limited to: a sub-6GHz band (e.g., 700 MHz communication frequency), mid-rangecommunication bands (e.g., 2.4 GHz), and mmWave bands (e.g., 24 GHz).Additionally or alternatively, the wireless communications connectionsmay support various modulation schemes, including but not limited to:filter bank multi-carrier (FBMC), the generalized frequency divisionmultiplexing (GFDM), universal filtered multi-carrier (UFMC)transmission, bi-orthogonal frequency division multiplexing (BFDM),sparse code multiple access (SCMA), non-orthogonal multiple access(NOMA), multi-user shared access (MUSA), and faster-than-Nyquist (FTN)signaling with time-frequency packing. Such frequency bands andmodulation techniques may be a part of a standards framework, such asLong Term Evolution (LTE) or other technical specification published byan organization like 3GPP or IEEE, which may include variousspecifications for subcarrier frequency ranges, a number of subcarriers,uplink/downlink transmission speeds, TDD/FDD, and/or other aspects ofwireless communication protocols.

The system 700 may depict aspects of a radio access network (RAN), andsystem 700 may be in communication with or include a core network (notshown). The core network may include one or more serving gateways,mobility management entities, home subscriber servers, and packet datagateways. The core network may facilitate user and control plane linksto mobile devices via the RAN, and it may be an interface to an externalnetwork (e.g., the Internet). Base stations 710, communication devices720, and small cells 730 may be coupled with the core network or withone another, or both, via wired or wireless backhaul links (e.g., S1interface, X2 interface, etc.).

The system 700 may provide communication links connected to devices or“things,” such as sensor devices, e.g., solar cells 737, to provide anIoT framework, Connected things within the IOT may operate withinfrequency bands licensed to and controlled by cellular network serviceproviders, or such devices or things may. Such frequency bands andoperation may be referred to as narrowband IoT (NB-IoT) because thefrequency bands allocated for IoT operation may be small or narrowrelative to the overall system bandwidth. Frequency bands allocated forNB-IoT may have bandwidths of 1, 5, 10, or 2.0 MHz, for example.

Additionally or alternatively, the IoT may include devices or thingsoperating at different frequencies than traditional cellular technologyto facilitate use of the wireless spectrum. For example, an IoTframework may allow multiple devices in system 700 to operate at a sub-6GHz band or other industrial, scientific, and medical (ISM) radio bandswhere devices may operate on a shared spectrum for unlicensed uses. Thesub-6 GHz band may also be characterized as and may also becharacterized as an NB-IoT band. For example, in operating at lowfrequency ranges, devices providing sensor data for “things,” such assolar cells 737, may utilize less energy, resulting in power-efficiencyand may utilize less complex signaling frameworks, such that devices maytransmit asynchronously on that sub-6 GHz band. The sub-6 GHz band maysupport a wide variety of uses case, including the communication ofsensor data from various sensors devices. Examples of sensor devicesinclude sensors for detecting energy, heat, light, vibration, biologicalsignals (e.g., pulse, EEG, EKG, heart rate, respiratory rate, bloodpressure), distance, speed, acceleration, or combinations thereof.Sensor devices may be deployed on buildings, individuals, and/or inother locations in the environment. The sensor devices may communicatewith one another and with computing systems which may aggregate and/oranalyze the data provided from one or multiple sensor devices in theenvironment.

In such a 5G framework, devices may perform functionalities performed bybase stations in other mobile networks (e.g., UMTS or LTE), such asforming a connection or managing mobility operations between nodes(e.g., handoff or reselection). For example, mobile device 715 mayreceive sensor data from the user utilizing the mobile device 715, suchas blood pressure data, and may transmit that sensor data on anarrowband IoT frequency band to base station 710. In such an example,some parameters for the determination by the mobile device 715 mayinclude availability of licensed spectrum, availability of unlicensedspectrum, and/or time-sensitive nature of sensor data. Continuing in theexample, mobile device 715 may transmit the blood pressure data becausea narrowband IoT band is available and can transmit the sensor dataquickly, identifying a time-sensitive component to the blood pressure(e.g., if the blood pressure measurement is dangerously high or low,such as systolic blood pressure is three standard deviations from norm).

Additionally or alternatively, mobile device 715 may formdevice-to-device (D2D) connections with other mobile devices or otherelements of the system 700, For example, the mobile device 715 may formRFID, WiFi, MultiFire, Bluetooth, or Zigbee connections with otherdevices, including communication device 720 or vehicle 745. In someexamples, D2D connections may be made using licensed spectrum bands, andsuch connections may be managed by a cellular network or serviceprovider. Accordingly, while the above example was described in thecontext of narrowband IoT, it can be appreciated that otherdevice-to-device connections may be utilized by mobile device 715 toprovide information (e.g., sensor data) collected on different frequencybands than a frequency band determined by mobile device 715 fortransmission of that information.

Moreover, some communication devices may facilitate ad-hoc networks, forexample, a network being formed with communication devices 720 attachedto stationary objects (e.g., lampposts in FIG. 7) and the vehicles 740,745, without a traditional connection to a base station 710 and/or acore network necessarily being formed. Other stationary objects may beused to support communication devices 720, such as, but not limited to,trees, plants, posts, buildings, blimps, dirigibles, balloons, streetsigns, mailboxes, or combinations thereof. In such a system 700,communication devices 720 and small cell 730 (e.g., a small cell.femtocell, WLAN access point, cellular hotspot, etc.) may be mountedupon or adhered to another structure, such as lampposts and buildings tofacilitate the formation of ad-hoc networks and other IoT-basednetworks. Such networks may operate at different frequency bands thanexisting technologies, such as mobile device 715 communicating with basestation 710 on a cellular communication band.

The communication devices 720 may form wireless networks, operating ineither a hierarchal or ad-hoc network fashion, depending, in part, onthe connection to another element of the system 700. For example, thecommunication devices 720 may utilize a 700 MHz communication frequencyto form a connection with the mobile device 715 in an unlicensedspectrum, while utilizing a licensed spectrum communication frequency toform another connection with the vehicle 745. Communication devices 720may communicate with vehicle 745 on a licensed spectrum to providedirect access for time-sensitive data, for example, data for anautonomous driving capability of the vehicle 745 on a 5.9 GHz band ofDedicated Short Range Communications (DSRC).

Vehicles 740 and 745 may form an ad-hoc network at a different frequencyband than the connection between the communication device 720 and thevehicle 745. For example, for a high bandwidth connection to providetime-sensitive data between vehicles 740, 745, a 24 GHz mmWave band maybe utilized for transmissions of data between vehicles 740, 745. Forexample, vehicles 740, 745 may share real-time directional andnavigation data with each other over the connection while the vehicles740, 745 pass each other across a narrow intersection line. Each vehicle740, 745 may be tracking the intersection line and providing image datato an image processing algorithm to facilitate autonomous navigation ofeach vehicle while each travels along the intersection line. In someexamples, this real-time data may also be substantially simultaneouslyshared over an exclusive, licensed spectrum connection between thecommunication device 720 and the vehicle 745, for example, forprocessing of image data received at both vehicle 745 and vehicle 740,as transmitted by the vehicle 740 to vehicle 745 over the 24 GHz mmWaveband. While shown as automobiles in FIG. 5, other vehicles may be usedincluding, but not limited to, aircraft, spacecraft, balloons, blimps,dirigibles, trains, submarines, boats, ferries, cruise ships,helicopters, motorcycles, bicycles, drones, or combinations thereof.

While described in the context of a 24 GHz mmWave band, it can beappreciated that connections may be formed in the system 700 in othermmWave bands or other frequency bands, such as 28 GHz, 37 GHz, 38 GHz,39 GHz, which may be licensed or unlicensed bands. In some cases,vehicles 740, 745 may share the frequency band that they arecommunicating on with other vehicles in a different network. Forexample, a fleet of vehicles may pass vehicle 740 and, temporarily,share the 24 GHz mmWave band to form connections among that fleet, inaddition to the 24 GHz mmWave connection between vehicles 740, 745. Asanother example, communication device 720 may substantiallysimultaneously maintain a 700 MHz connection with the mobile device 715operated by a user (e.g., a pedestrian walking along the street) toprovide information regarding a location of the user to the vehicle 745over the 5.9 GHz band. In providing such information, communicationdevice 720 may leverage antenna diversity schemes as part of a massiveMIMO framework to facilitate time-sensitive, separate connections withboth the mobile device 715 and the vehicle 745. A massive MIMO frameworkmay involve a transmitting and/or receiving devices with a large numberof antennas (e.g., 12, 20, 64, 128, etc.), which may facilitate precisebeamforming or spatial diversity unattainable with devices operatingwith fewer antennas according to legacy protocols (e.g., WiFi or LTE).

The base station 710 and small cell 730 may wirelessly communicate withdevices in the system 700 or other communication-capable devices in thesystem 700 having at the least a sensor wireless network, such as solarcells 737 that may operate on an active/sleep cycle, and/or one or moreother sensor devices. The base station 710 may provide wirelesscommunications coverage for devices that enter its coverages area, suchas the mobile device 715 and the drone 717. The small cell 730 mayprovide wireless communications coverage for devices that enter itscoverage area, such as near the building that the small cell 730 ismounted upon, such as vehicle 745 and drone 717.

Generally, a small cell 730 may be referred to as a small cell andprovide coverage for a local geographic region, for example, coverage of200 meters or less in some examples. This may be contrasted with atmacrocell, which may provide coverage over a wide or large area on theorder of several square miles or kilometers. In some examples, a smallcell 730 may be deployed (e.g., mounted on a building) within somecoverage areas of a base station 710 (e.g., a macrocell) where wirelesscommunications traffic may be dense according to a traffic analysis ofthat coverage area. For example, a small cell 730 may be deployed on thebuilding in FIG. 7 in the coverage area of the base station 710 if thebase station 710 generally receives and/or transmits a higher amount ofwireless communication transmissions than other coverage areas of thatbase station 710. A base station 710 may be deployed in a geographicarea to provide wireless coverage for portions of that geographic area.As wireless communications traffic becomes more dense, additional basestations 710 may be deployed in certain areas, which may alter thecoverage area of an existing base station 710, or other support stationsmay be deployed, such as a small cell 730. Small cell 730 may be afemtocell, which may provide coverage for an area smaller than a smallcell (e.g., 100 meters or less in some examples (e.g., one story of abuilding)).

While base station 710 and small cell 730 may provide communicationcoverage for a portion of the geographical area surrounding theirrespective areas, both may change aspects of their coverage tofacilitate faster wireless connections for certain devices. For example,the small cell 730 may primarily provide coverage for devicessurrounding or in the building upon which the small cell 730 is mounted.However, the small cell 730 may also detect that a device has entered iscoverage area and adjust its coverage area to facilitate a fasterconnection to that device.

For example, a small cell 730 may support a massive MIMO connection withthe drone 717, which may also be referred to as an unmanned aerialvehicle (UAV), and, when the vehicle 745 enters it coverage area, thesmall cell 730 adjusts some antennas to point directionally in adirection of the vehicle 745, rather than the drone 717, to facilitate amassive MIMO connection with the vehicle, in addition to the drone 717.In adjusting some of the antennas, the small cell 730 may not support asfast as a connection to the drone 717, as it had before the adjustment.However, the drone 717 may also request a connection with another device(e.g., base station 710) in its coverage area that may facilitate asimilar connection as described with reference to the small cell 730, ora different (e.g., faster, more reliable) connection with the basestation 710. Accordingly, the system 700 may enhance existingcommunication links in providing additional connections to devices thatmay utilize or demand such links. For example, the small cell 730 mayinclude a massive MIMO system that directionally augments a link tovehicle 745, with antennas of the small cell directed to the vehicle 745for a specific time period, rather than facilitating other connectionsthe small cell 730 connections to the base station 710, drone 717, orsolar cells 737). In some examples, drone 717 may serve as a movable oraerial base station.

The wireless communications system 700 may include devices such as basestation 710, communication device 720, and small cell 730 that maysupport several connections to devices in the system 700. Such devicesmay operate in a hierarchal mode or an ad-hoc mode with other devices inthe network of system 700. While described in the context of a basestation 710, communication device 720, and small cell 730, it can beappreciated that other devices that can support several connections withdevices in the network may be included in system 700, including but notlimited to: macrocells, femtocells, routers, satellites, and RFDdetectors.

In various examples, the elements of wireless communication system 700,such as base station 710, a mobile device 715, a drone 717,communication device 720 a small cell 730, and vehicles 740, 745, may beimplemented utilizing an autocorrelation calculator as described herein.For example, the communication device 720 may include system 100 in FIG.1, electronic device 202 in FIG. 2, system 400 in FIG. 4. For example,the communication device 720 may be implemented as the electronic device202. In various examples, the elements of communication system 700 maybe implemented using, for example, system 100 in FIG. 1, electronicdevice 202 in FIG. 2, system 400 in FIG. 4, or any system or combinationof the systems depicted in FIGS. 1-2 and 4-8 described herein.

FIG. 8 is a block diagram of a wireless communications system 800 inaccordance with aspects of the present disclosure. The wirelesscommunications system 800 includes a mobile device 815, a drone 817, acommunication device 820, and a small cell 830. A building 810 alsoincludes devices of the wireless communication system 800 that may beconfigured to communicate with other elements in the building 810 or thesmall cell 830. The building 810 includes networked workstations 840,845, virtual reality device 850, IoT devices 855, 860, and networkedentertainment device 865. In the depicted system 800, IoT devices 855,860 may be a washer and dryer, respectively, for residential use, beingcontrolled by the virtual reality device 850. Accordingly, while theuser of the virtual reality device 850 may be in different room of thebuilding 810, the user may control an operation of the IoT device 855,such as configuring a washing machine setting. Virtual reality device850 may also control the networked entertainment device 865. Forexample, virtual reality device 850 may broadcast a virtual game beingplayed by a user of the virtual reality device 850 onto a display of thenetworked entertainment device 865.

The small cell 830 or any of the devices of building 810 may beconnected to a network that provides access to the Internet andtraditional communication links. Like the system 700, the system 800 mayfacilitate a wide-range of wireless communications connections in a 5Gsystem that may include various frequency bands, including but notlimited to: a sub-6 GHz band (e.g., 700 MHz communication frequency),mid-range communication bands (e.g., 2.4 GHz), and mmWave bands (e.g.,24 GHz). Additionally or alternatively, the wireless communicationsconnections may support various modulation schemes as described abovewith reference to system 700. System 800 may operate and be configuredto communicate analogously to system 700. Accordingly, similarlynumbered elements of system 800 and system 700 may be configured in ananalogous way, such as communication device 820 to communication device720, small cell 830 to small cell 730, etc.

Like the system 700, where elements of system 700 are configured to formindependent hierarchal or ad-hoc networks, communication device 820 mayform a hierarchal network with small cell 830 and mobile device 815,while an additional ad-hoc network may be formed among the small cell830 network that includes drone 817 and some of the devices of thebuilding 810, such as networked workstations 840, 845 and IoT devices855, 860.

Devices in communication system 800 may also form (D2D) connections withother mobile devices or other elements of the system 800. For example,the virtual reality device 850 may form a narrowband IoT connectionswith other devices, including IoT device 855 and networked entertainmentdevice 865. As described above, in some examples, D2D connections may bemade using licensed spectrum bands, and such connections may be managedby a cellular network or service provider. Accordingly, while the aboveexample was described in the context of a narrowband IoT, it can beappreciated that other device-to-device connections may be utilized byvirtual reality device 850.

In various examples, the elements of wireless communication system 800,such as the mobile device 815, the drone 817, the communication device820, and the small cell 830, the networked workstations 840, 845, thevirtual reality device 850, the IoT devices 855, 860, and the networkedentertainment device 865, may be implemented utilizing anautocorrelation calculator as described herein. For example, thecommunication device 720 may include system 100 in FIG. 1, electronicdevice 202 in FIG. 2, system 400 in FIG. 4.

In an example, the mobile device 815 may implement the electronic device202 having an autocorrelation calculator 205 for receiving signals viathe antennas 206-210 and calculating autocorrelation matrices asdescribed herein. The signals received may be calibration signals todetermine a set of weights for the devices 815, which may be utilized togenerate an estimate of the information encoded in additional incomingsignals based on the determined set of weights. Advantageously, indetermining a set of weights more quickly with the autocorrelationcalculation techniques described herein, the mobile device 815 mayrender information (e.g., video content) more quickly than a mobiledevice 815 employing a traditional autocorrelation calculation scheme.For example, the mobile device 815, employing an autocorrelationcalculator 205, may utilize a lesser amount of memory than anautocorrelation calculation occupying an N×L amount of memory. Themobile device 815 may occupy a memory space related to a number ofantennas on the mobile device 815. The mobile device 815 may store anautocorrelation matrix of an L×L size of memory and a vector spacerepresentative of the symbols indicative of RF energy received at eachrespective antenna. The amount of memory occupied in thisautocorrelation calculation may be less than that of memory occupiedwhen an autocorrelation is not computed at each time period.

According to an autocorrelation calculation described above where N timeperiods are received for each L antenna, an autocorrelation matrix,calculated according to traditional autocorrelation calculation scheme,may occupy an N×L amount of memory. Such an autocorrelation calculationmay utilize more memory in calculating the autocorrelation than theautocorrelation calculation, described herein, in which each receivedsignal vector in real-time is autocorrelated and added to a storedautocorrelation matrix representative of the autocorrelation at aprevious time period relative to a current, real-time, time period ofthe received signal. Advantageously, the memory available to the mobiledevice 815 may be efficiently utilized, allowing the mobile device 815to utilize other memory for additional processing operations, such asqueueing video content to be streamed to a user of the mobile device815.

While described above in the context of some specific examples of theelements of communication system 800, the elements of communicationsystem 800 may be implemented using, for example, system 100 in FIG. 1,electronic device 202 in FIG. 2, system 400 in FIG. 4, or any system orcombination of the systems depicted in FIGS. 1-2 and 4-8 describedherein.

Certain details are set forth above to provide a sufficientunderstanding of described examples. However, it will be clear to oneskilled in the art that examples may be practiced without various ofthese particular details. The description herein, in connection with theappended drawings, describes example configurations and does notrepresent all the examples that may be implemented or that are withinthe scope of the claims. The terms “exemplary” and “example” as may beused herein means “serving as an example, instance, or illustration,”and not “preferred” or “advantageous over other examples.” The detaileddescription includes specific details for the purpose of providing anunderstanding of the described techniques. These techniques, however,may be practiced without these specific details. In some instances,well-known structures and devices are shown in block diagram form inorder to avoid obscuring the concepts of the described examples.

Information and signals described herein may be represented using any ofa variety of different technologies and techniques. For example, data,instructions, commands, information, signals, bits, symbols, and chipsthat may be referenced throughout the above description may berepresented by voltages, currents, electromagnetic waves, magneticfields or particles, optical fields or particles, or any combinationthereof.

Techniques described herein may be used for various wirelesscommunications systems, which may include multiple access cellularcommunication systems, and which may employ code division multipleaccess (CDMA), time division multiple access (TDMA), frequency divisionmultiple access (FDMA), orthogonal frequency division multiple access(OFDMA), or single carrier frequency division multiple access (SC-FDMA),or any a combination of such techniques. Some of these techniques havebeen adopted in or relate to standardized wireless communicationprotocols by organizations such as Third Generation Partnership Project(3GPP), Third Generation Partnership Project 2 (3GPP2) and IEEE. Thesewireless standards include Ultra Mobile Broadband (LIMB), UniversalMobile Telecommunications System (UMTS), Long Term Evolution (LTE),LTE-Advanced (LTE-A), LTE-A Pro, New Radio (NR), Nex GenerationArchitecture (NexGen), IEEE 802.11 (WiFi), and IEEE 802.16 (WiMAX),among others.

The terms “5G” or “5G communications system” may refer to systems thatoperate according to standardized protocols developed or discussedafter, for example, LTE Releases 13 or 14 or WiMAX 802.16e-2005 by theirrespective sponsoring organizations. The features described herein maybe employed in systems configured according to other generations ofwireless communication systems, including those configured according tothe standards described above.

The various illustrative blocks and modules described in connection withthe disclosure herein may be implemented or performed with ageneral-purpose processor, a digital signal processor (DSP), anapplication-specific integrated circuit ARC), a field-programmable gatearray (FPGA), or other programmable logic device, discrete gate ortransistor logic, discrete hardware components, or any combinationthereof designed to perform the functions described herein. Ageneral-purpose processor may be a microprocessor, but in thealternative, the processor may be any conventional processor,controller, microcontroller, or state machine. A processor may also beimplemented as a combination of computing devices (e.g., a combinationof a DSP and a microprocessor, multiple microprocessors, one or moremicroprocessors in conjunction with a DSP core, or any other suchconfiguration).

The functions described herein may be implemented in hardware, softwareexecuted by a processor, firmware, or any combination thereof. Ifimplemented in software executed by a processor, the functions may bestored on or transmitted over as one or more instructions or code on acomputer-readable medium. Computer-readable media includes bothnon-transitory computer storage media and communication media includingany medium that facilitates transfer of a computer program from oneplace to another. A non-transitory storage medium may be any availablemedium that can be accessed by a general purpose or special purposecomputer. By way of example, and not limitation, non-transitorycomputer-readable media can comprise RAM, ROM, electrically erasableprogrammable read only memory (EEPROM), or optical disk storage,magnetic disk storage or other magnetic storage devices, or any othernon-transitory medium that can be used to carry or store desired programcode means in the form of instructions or data structures and that canbe accessed by a general-purpose or special-purpose computer, or ageneral-purpose or special-purpose processor.

Also, any connection is properly termed a computer-readable medium. Forexample, if the software is transmitted from a website, server, or otherremote source using a coaxial cable, fiber optic cable, twisted pair,digital subscriber line (DSL), or wireless technologies such asinfrared, radio, and microwave, then the coaxial cable, fiber opticcable, twisted pair, DSL, or wireless technologies such as infrared,radio, and microwave are included in the definition of medium.Combinations of the above are also included within the scope of cornpater-readable media.

Other examples and implementations are within the scope of thedisclosure and appended claims. For example, due to the nature ofsoftware, functions described above can be implemented using softwareexecuted by a processor, hardware, firmware, hardwiring, or combinationsof any of these. Features implementing functions may also be physicallylocated at various positions, including being distributed such thatportions of functions are implemented at different physical locations.

Also, as used herein, including in the claims, “or” as used in a list ofitems (for example, a list of items prefaced by a phrase such as “atleast one of” or “one or more of”) indicates an inclusive list suchthat, for example, a list of at least one of A, B, or C means A or B orC or AB or AC or BC or ABC (i.e., A and B and C). Also, as used herein,the phrase “based on” shall not be construed as a reference to a closedset of conditions. For example, an exemplary step that is described as“based on condition A” may be based on both a condition A and acondition B without departing from the scope of the present disclosure.In other words, as used herein, the phrase “based on” shall be construedin the same manner as the phrase “based at least in part on.”

From the foregoing it will be appreciated that, although specificexamples have been described herein for purposes of illustration,various modifications may be made while remaining with the scope of theclaimed technology. The description herein is provided to enable aperson skilled in the art to make or use the disclosure. Variousmodifications to the disclosure will be readily apparent to thoseskilled in the art, and the generic principles defined herein may beapplied to other variations without departing from the scope of thedisclosure. Thus, the disclosure is not limited to the examples anddesigns described herein, but is to be accorded the broadest scopeconsistent with the principles and novel features disclosed herein.

What is claimed is:
 1. An apparatus comprising a processor configuredto: determine a first autocorrelation matrix representative, in part, ofan autocorrelation of symbols comprising symbols indicative of firstradio frequency (RF) signal and symbols indicative of a second RFsignal, the first and second RF signals received from a wireless channelduring a first time period; store the first autocorrelation matrix in aplurality of memory cells; and determine a second autocorrelation matrixbased on the first autocorrelation matrix and an autocorrelation ofsymbols comprising symbols indicative of a third. RF signal and symbolsindicative of a fourth RF signal, the third and fourth RF signalsreceived from the wireless channel during a second time periodsubsequent to the first time period.
 2. The apparatus of claim I.wherein the processor is further configured to: store the secondautocorrelation matrix; determine a third autocorrelation matrix basedon the second autocorrelation matrix and an autocorrelation of symbolscomprising symbols indicative of fifth RF signal and symbols indicativeof sixth RF signal, the fifth and sixth RF signals received from thewireless channel during a third time period subsequent to the secondtime period.
 3. The apparatus of claim 2, wherein the processor isconfigured to store the second autocorrelation matrix at a memorylocation where the first autocorrelation matrix was stored.
 4. Theapparatus of claim 1, wherein the processor is further coupled to afirst receive path and a second receive path, the processor is furtherconfigured to: receive the first RF signal and the third RF signal atthe first receive path; and receive the second RF signal and the fourthRF signal at the second receive path.
 5. The apparatus of claim 4,wherein the symbols indicative of the third RF signal and the symbolsindicative of the fourth RF signal are converted from frequency-domainsymbols.
 6. The apparatus of claim 5, wherein the frequency-domainsymbols include frequency-domain OFDM symbols.
 7. The apparatus of claim1, wherein the first, second, third and fourth RF signals eachrepresents a symbol indicative of RF energy received in a portion of awireless spectrum incident on an antenna.
 8. At least one non-transitorycomputer-readable storage medium containing programming instructionsthat, when executed by a processor, cause the processor to: store anautocorrelation matrix representative of an autocorrelation of symbolscomprising symbols indicative of a first radio frequency (RF) signal andsymbols indicative of a second RF signal, the first and second RFsignals received from a wireless channel during a first time period; andupdate the autocorrelation matrix by autocorrelation of symbolscomprising symbols indicative of a third RF signal and symbolsindicative of a fourth RF signal, the third and fourth RF signalsreceived from the wireless channel during a second time periodsubsequent to the first time period.
 9. The computer-readable storagemedium of claim 8, wherein the processor is further configured to:update the autocorrelation matrix by autocorrelation of symbolscomprising symbols indicative of fifth RF signal and symbols indicativeof sixth RF signal, the fifth and sixth RF signals received from thewireless channel during a third time period subsequent to the secondtime period.
 10. The computer-readable storage medium of claim 8,wherein the processor is further coupled to a first receive path and asecond receive path, the processor is further configured to: receive thefirst RF signal and the third RF signal at the first receive pathassociated with a first antenna; and receive the second RF signal andthe fourth RF signal at the second receive path associated with a secondantenna.
 11. The computer-readable storage medium of claim 8, whereinthe symbols indicative of the first, second, third and fourth RF signalsare converted from frequency-domain symbols including frequency-domainOFDM symbols.
 12. The computer-readable storage medium of claim 10,wherein: the symbols indicative of the first RF signal and the symbolsindicative of the second RF signal form a first vector, in which eachcomponent represents a symbol indicative of RF energy received in aportion of a wireless spectrum incident on the first antenna; and thesymbols indicative of the third RF signal and the symbols indicative ofthe fourth RF signal form a second vector, in which each componentrepresents a symbol indicative of RF energy received in a portion of awireless spectrum incident on the second antenna.
 13. Thecomputer-readable storage medium of claim 8, wherein the programminginstructions for execution by the processor are retrieved from a networkvia an I/O interface, and wherein the processor is configured to storeand update the autocorrelation matrix at a plurality of memory cells ina memory device.
 14. A method comprising: receiving, at a plurality ofreceive paths, a plurality of first radio frequency (RF) signals at afirst time; determining, by a processor, an autocorrelation matrixrepresentative, in part, of an autocorrelation of symbols representingthe plurality of first RF signals; receiving, at the plurality ofreceive paths, a plurality of second radio frequency (RF) signals at asecond time subsequent to the first time; and updating, by theprocessor, the autocorrelation matrix based on an autocorrelation ofsymbols representing the plurality of second RF signals.
 15. The methodof claim 14, wherein each of the plurality of receive paths isassociated with a respective antenna.
 16. The method of claim 14,wherein the plurality of first RF signals and the plurality of second RFsignals comprise frequency-domain symbols including OFDM symbols. 17.The method of claim 16 further comprising: converting the plurality offirst RF signals to time-domain symbols before determining theautocorrelation matrix; and converting the plurality of second RFsignals to time-domain symbols before updating the autocorrelationmatrix.
 18. The method of claim 14, wherein updating the autocorrelationmatrix comprises adding the autocorrelation matrix by theautocorrelation of symbols representing the plurality of second RFsignals.
 19. The method of claim 18, wherein each of the plurality offirst RF signals and the plurality of second RF signals comprise arespective vector having a size based at least on a number of receivepaths in the plurality of receive paths.
 20. The method of claim 19,wherein a size of the autocorrelation matrix is based at least on thenumber of receive paths in the plurality of receive paths.